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12x+9-4x-4=3x-7-X+30

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3 Answers

Hi again Pj;
12x+9-4x-4=3x-7-x+30
Let's combine like terms on both sides...
(12x-4x)+(9-4)=(3x-x)+(-7+30)
8x+5=2x+23
Let's isolate x...
Let's subtract 5 from both sides...
-5+8x+5=2x+23-5
8x=2x+18
Let's subtract 2x from both sides...
-2x+8x=2x+18-2x
6x=18
Let's divide both sides by 6...
(6x)/6=18/6
x=3
 
Let's check our results in the original equation...
12x+9-4x-4=3x-7-x+30
Let's substitute x with 3...
[12(3)]+9-[4(3)]-4=[3(3)]-7-(3)+30
36+9-12-4=9-7-3+30
45-16=2+27
29=29
It works!
 
PJ,
 
This equation isn't too bad. Just a couple steps and I bet you'll recognize what to do quickly.
 
12x+9-4x-4 = 3x-7-x+30
 
 
Step 1) Combine like terms 
*If I think of the equation as having a left side and a right side (split by the = sign), I'm going to combine the similar terms on the left and right.
 
LEFT: 12x+9-4x-4  ---->8x+5          (I did 12x-4x and 9-4)
 
RIGHT: 3x-7-x+30 -----> 2x+23       (3x-1x and -7+30)
 
So now we have 8x+5 = 2x+23   (The variable is on both sides of the = sign) (Not good)
 
Step 2) Eliminate one of the variables
 
8x+5 = 2x+23   (I'm going to subtract 2x from both sides to get rid of one variable
-2x      -2x
 
6x+5 = 23   (Now it's just a two-step equation, easy!)
    -5     -5
 
6x=18  -----> x=3
 
**Don't forget to check!
 
12(3)+9-4(3)-4   =  3(3)-7-3+30
 
29 = 29 (Correct!)
To solve this equation, we need to combine all of constants and the x terms on each side of the equation:
 
12x + 9 - 4x - 4 = 3x - 7 - x + 30
 
8x + 5 = 2x + 23
 
Now, we subtract 5 from both sides and subtract 2x from both sides:
 
6x = 18
 
Now we divide both sides by 6
 
x = 18/6
 
x = 3